Question

Num triângulo ABC sabe-se que Â= 45°, B=60°, e a=5cm. Calcule o perímetro do triângulo. (Sen 75° = 0.966)

Answer 1

Resposta:

P = 17,225 cm

Explicação passo a passo:

Lei dos senos

a/sen A = b / sen b = c / sen c

A/sen 45° = b/sen 60° = c / sen 75°

5 / \/2/2 = b / \/3 /2 = c / 0,966

5 / \/2/2 = 5.2/ \/2 = 10/ \/2

10/ \/2 = b/ \/3 /2

10/ \/2 = c /0,966

5. 2 / \/2 = c / 0,966

10 / \/2 = c / 0,966

10 . 0,966 = \/2 . c

9,66 = \/2 . c

9,66 / \/2 = c

C = 9,66 / \/2

C = 9,66 / 1,414

C = 6,83

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5.2/ \/2 = b . 2 / \/3

10/ \/2 = 2b / \/3

5 / \/2 = b / \/3

5 . \/3 / \/2 = b

b = 5 \/3 / \/2 . \/2 / \/2

b = 5\/6 / 2

P = a + b + c

P = 5 + 5\/6/2 + 6,85

P = 5 + 2,5 . 2,45 + 6,831

P = 5 + 6,125 + 6,831

P = 11,125 + 6,831

P = 17,956 cm